This handy Spectrum Math Grade 7 Answer Key Chapter 6 Pretest provides detailed answers for the workbook questions

Check What You Know

Tell if each is an example of a sample or a population.

Question 1.
a. 10 students’ heights are measured
sample.

Explanation:
A sample is the specific group that you will collect data from.
The size of the sample is always less than the total size of the population.
Therefore, sample of 10 students’ heights are measured.

b. every student’s time of arrival at school is recorded
population.

Explanation:
A population is the entire group that you want to draw conclusions about.
A population consists of sets of observations, objects etc., that are all something in common.
So, every student’s time of arrival at school is recorded is population.

Question 2.
a. every 5th water bottle is checked
sample.

Explanation:
A sample is the specific group that you will collect data from.
The size of the sample is always less than the total size of the population.
So, sample is, every 5th water bottle is checked.

b. a teacher records all students’ test grades
population.

Explanation:
A population is the entire group that you want to draw conclusions about.
A population consists of sets of observations, objects etc., that are all something in common.
Therefore, a teacher records all students’ is population.

Tell if each sample would be considered random or biased.

Question 3.
Felicia wants to know what middle school students’ favorite sports are. She asks 20 people leaving a football game.
biased sampling.

Explanation:
A biased sample does not accurately represent all elements of the population.
Sampling bias occurs when some members of a population are systematically or more likely to be selected in a sample than others.
So, Felicia asks 20 people leaving a football game is a biased sampling.

Question 4.
Mr. Walsh puts every 7th grader’s name into ajar. He shakes the jar and pulls out 4 students’ names.
random sampling.

Explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population which is also called probability.
So, the above given information is a random sampling.

Complete the following items based on the data set below.

Joe records the daily high temperature every other day for one month. This is the information he collects about the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81,73, 82, 69, 73, 74

Question 5.
Create a stem-and-leaf plot for the data.

Explanation:
Given, the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81,73, 82, 69, 73, 74
Stem and leaf plots display the shape and spread of a continuous data distribution.
These graphs are similar to histograms.
stem 6 – 66, 67, 68, 68, 69 (leafs)
stem 7 – 72, 73, 73,73, 74, 79 (leafs)
stem 8 – 81, 82, 82, 85 (leafs)

Question 6.
Find the mean, median, mode, and range of the data.
mean: _______________
mode: _______________
median: _______________
range: _______________
mean: 74.13
mode: 73
median: 73
range: 19

Explanation:
Given set of date,
66, 68, 72, 79, 67, 82, 73, 85, 68, 81,73, 82, 69, 73, 74
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85
mean:
The mean is the average of a set of numbers.
sum of 66, 68, 72, 79, 67, 82, 73, 85, 68, 81,73, 82, 69, 73, 74 = 1112
mean = $$\frac{1112}{15}$$ = 74.13
median :
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an odd amount of numbers, the middle number is the median.
Arrange the numbers from least to greatest to find median.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85
mode:
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85
range :
The range is the difference between the greatest and least numbers in the set.
Arrange the numbers from least to greatest to find range.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85
85 – 66 = 19

Continue using the data set below to answer the questions.

Joe records the daily hi9h temperature every other day for one month. This is the information he collects about the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81, 73, 82, 69, 73, 74

Question 7.
How many days from the sample were above 70 degrees?
10 days from the sample were above 70 degrees.

Explanation:
Given, the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81, 73, 82, 69, 73, 74.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85 arranged in ascending order.
So, 10 days from the sample were above 70 degrees.

Question 8.
What percentage of days from the sample were 69 degrees or less?
33.33%

Explanation:
Given, the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81, 73, 82, 69, 73, 74.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85 arranged in ascending order.
$$\frac{5}{15}$$ x 100% = 33.33%

Question 9.
Based on a 30-day month, how many days were most likely above 80 degrees?
8

Explanation:
Given, the daily high temperature in Fahrenheit:
66, 68, 72, 79, 67, 82, 73, 85, 68, 81, 73, 82, 69, 73, 74.
66, 67, 68, 68, 69, 72, 73, 73, 73, 74, 79, 81, 82, 82, 85 arranged in ascending order.
for 15 days, only 4 days above 80 degrees high temperature in Fahrenheit.
Based on a 30-day month,
2 x 4 = 8 days above 80 degrees.

Use the two data sets below to answer the questions.

Juanita gathered information about the sizes of oranges and grapefruits. She chose 10 of each from the grocery store to weigh.

Question 10.
Draw a histogram for each set of data.

Explanation:
We know that,
A histogram is a graphical representation of discrete or continuous data.
The area of a bar in a histogram is equal to the frequency.
The y -axis is plotted by frequency density and the x -axis is plotted with the range of values divided into intervals.
Therefore the above histogram shows that, Juanita gathered information about the sizes of oranges and grapefruits.

Question 11.
Find the measures of center and range for each set of data.
a. mean: ______________________
median: ______________________
mode: ______________________
range:______________________
a.
mean: 7.31
median: 7.35
mode: 7.2 and 7.5
range:1.3

Explanation:
Mean:
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
sum = 7.0 + 7.5 + 7.2 + 6.5 + 7.8 + 7.3 + 7.4 + 7.7 + 7.5 + 7.2 = 73.1
mean or avg = $$\frac{73.1}{10}$$ = 7.31
Median:
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, take the of the two middle number.
Arrange the numbers from least to greatest to find median.
6.5, 7.0, 7.2, 7.2, 7.3, 7.4, 7.5, 7.5, 7.7, 7.8
median = $$\frac{7.3 + 7.4}{2}$$ = 7.35
mode:
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
6.5, 7.0, 7.2, 7.2, 7.3, 7.4, 7.5, 7.5, 7.7, 7.8
7.2 and 7.5 is the mode of the given data
range:
the difference between the staring and ending points.
Arrange the numbers from least to greatest to find range.
6.5, 7.0, 7.2, 7.2, 7.3, 7.4, 7.5, 7.5, 7.7, 7.8
range = 6.5 – 7.8 = 1.3

b. mean: ______________________
median: ______________________
mode: ______________________
range:______________________
mean: 9.54
median: 9.55
mode: 8.9 and 9.6
range: 1.3

Explanation:
Mean:
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
sum = 10.2 + 8.9 + 9.4 + 9.5 + 10.0 + 8.9 + 9.2 + 9.6 + 10.1 + 9.6 = 95.4
mean or avg = $$\frac{95.4}{10}$$ = 9.54
Median:
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, then take the average of the middle numbers.
Arrange the numbers from least to greatest to find median.
8.9, 8.9, 9.2, 9.4, 9.5, 9.6, 9.6,10.0, 10.1, 10.2
median = $$\frac{9.5 + 9.6}{2}$$ = 9.55
mode:
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
8.9, 8.9, 9.2, 9.4, 9.5, 9.6, 9.6,10.0, 10.1, 10.2
8.9 and 9.6 is the mode of the given data
range:
the difference between the staring and ending points.
Arrange the numbers from least to greatest to find range.
8.9, 8.9, 9.2, 9.4, 9.5, 9.6, 9.6,10.0, 10.1, 10.2
range = 6.5 – 7.8 = 1.3

Question 12.
Tell one way the data sets are alike and one way they are different.
alike: _______________________
different: _________________