Question

steps for statistical questions
fill in the blanks below:
the ____ of
a numerical set of data
is the difference of the
greatest value and the
least value.
the ____ of
a numerical set of data
is the middle number
when the numbers are
written in numerical
order.
the ____ of
a numerical set of data
is the value that occurs
most frequently.
the ____ is
the average of a set of
data, calculated by
dividing their sum by
the number of data
points.
find the mean, median, mode(s), and range of the following data. round all answers to two
decimal places.

1. social media followers (in hundreds): 5, 3, 8, 5, 12, 3, 5

mean: __ median: mode: range: __

1. video game hours per week: 15, 8, 12, 20, 8, 25, 12

mean: __ median: mode: range: __

1. test scores: 85, 92, 78, 94, 88, 91

mean: __ median: mode: range: __

1. streaming service subscriptions: 3, 5, 2, 7, 4, 6

mean: __ median: mode: range: __

1. monthly coffee shop visits: 12, 8, 15, 20, 18, 10, 25

mean: __ median: mode: range: __
real - world application problems

1. tiktok video views the number of views (in thousands) on your last 8 tiktok videos:

15, 32, 28, 19, 25, 31, 22, 18
a. what is the range of video views?
b. find the mean, median, and mode(s) of the video views.

Answer:

Problem 1: Social Media Followers (in hundreds): 5, 3, 8, 5, 12, 3, 5

Step 1: Sort the data

Sorted data: \( 3, 3, 5, 5, 5, 8, 12 \)

Step 2: Calculate Mean

Sum of data: \( 3 + 3 + 5 + 5 + 5 + 8 + 12 = 41 \)
Number of data points: \( 7 \)
Mean: \( \frac{41}{7} \approx 5.86 \) (rounded to two decimal places)

Step 3: Calculate Median

Middle term (4th term in sorted data): \( 5 \)

Step 4: Calculate Mode

Most frequent value: \( 5 \) (appears 3 times)

Step 5: Calculate Range

Greatest value - Least value: \( 12 - 3 = 9 \)

Problem 2: Video Game Hours Per Week: 15, 8, 12, 20, 8, 25, 12

Step 1: Sort the data

Sorted data: \( 8, 8, 12, 12, 15, 20, 25 \)

Step 2: Calculate Mean

Sum of data: \( 8 + 8 + 12 + 12 + 15 + 20 + 25 = 100 \)
Number of data points: \( 7 \)
Mean: \( \frac{100}{7} \approx 14.29 \) (rounded to two decimal places)

Step 3: Calculate Median

Middle term (4th term in sorted data): \( 12 \)

Step 4: Calculate Mode

Most frequent values: \( 8, 12 \) (each appears 2 times)

Step 5: Calculate Range

Greatest value - Least value: \( 25 - 8 = 17 \)

Problem 3: Test Scores: 85, 92, 78, 94, 88, 91

Step 1: Sort the data

Sorted data: \( 78, 85, 88, 91, 92, 94 \)

Step 2: Calculate Mean

Sum of data: \( 78 + 85 + 88 + 91 + 92 + 94 = 528 \)
Number of data points: \( 6 \)
Mean: \( \frac{528}{6} = 88.00 \)

Step 3: Calculate Median

Average of 3rd and 4th terms: \( \frac{88 + 91}{2} = 89.50 \)

Step 4: Calculate Mode

No value repeats, so no mode.

Step 5: Calculate Range

Greatest value - Least value: \( 94 - 78 = 16 \)

Problem 4: Streaming Service Subscriptions: 3, 5, 2, 7, 4, 6

Step 1: Sort the data

Sorted data: \( 2, 3, 4, 5, 6, 7 \)

Step 2: Calculate Mean

Sum of data: \( 2 + 3 + 4 + 5 + 6 + 7 = 27 \)
Number of data points: \( 6 \)
Mean: \( \frac{27}{6} = 4.50 \)

Step 3: Calculate Median

Average of 3rd and 4th terms: \( \frac{4 + 5}{2} = 4.50 \)

Step 4: Calculate Mode

No value repeats, so no mode.

Step 5: Calculate Range

Greatest value - Least value: \( 7 - 2 = 5 \)

Problem 5: Monthly Coffee Shop Visits: 12, 8, 15, 20, 18, 10, 25

Step 1: Sort the data

Sorted data: \( 8, 10, 12, 15, 18, 20, 25 \)

Step 2: Calculate Mean

Sum of data: \( 8 + 10 + 12 + 15 + 18 + 20 + 25 = 108 \)
Number of data points: \( 7 \)
Mean: \( \frac{108}{7} \approx 15.43 \) (rounded to two decimal places)

Step 3: Calculate Median

Middle term (4th term in sorted data): \( 15 \)

Step 4: Calculate Mode

No value repeats, so no mode.

Step 5: Calculate Range

Greatest value - Least value: \( 25 - 8 = 17 \)

Problem 6: TikTok Video Views (in thousands): 15, 32, 28, 19, 25, 31, 22, 18

Part a: Range

Step 1: Find greatest and least values

Greatest value: \( 32 \), Least value: \( 15 \)

Step 2: Calculate Range

\( 32 - 15 = 17 \)

Part b: Mean, Median, Mode

Step 1: Sort the data

Sorted data: \( 15, 18, 19, 22, 25, 28, 31, 32 \)

Step 2: Calculate Mean

Sum of data: \( 15 + 18 + 19 + 22 + 25 + 28 + 31 + 32 = 190 \)
Number of data points: \( 8 \)
Mean: \( \frac{190}{8} = 23.75 \)

Step 3: Calculate Median

Average of 4th and 5th terms: \( \frac{22 + 25}{2} = 23.50 \)

Step 4: Calculate Mode

No value repeats, so no mode.

Final Answers

Problem 1

Mean: \( \boldsymbol{5.86} \), Median: \( \boldsymbol{5} \), Mode: \( \boldsymbol{5} \), Range: \( \boldsymbol{9} \)

Problem 2

Mean: \( \boldsymbol{14.29} \), Median: \( \boldsymbol{12} \), Mode: \( \boldsymbol{8, 12} \), Range: \( \boldsymbol{17} \)

Problem 3

Mean: \( \boldsymbol{88.00} \), Median: \( \boldsymbol{89.50} \), Mode: \( \boldsymbol{\text{No Mode}} \), Range: \( \boldsymbol{16} \)

Problem 4

Mean: \( \boldsymbol{4.50} \), Median: \( \boldsymbol{4.50} \), Mode: \( \boldsymbol{\text{No Mode}} \), Range: \( \boldsymbol{5} \)

Problem 5

Mean: \( \boldsymbol{15.43} \), Median: \( \boldsymbol{15} \), Mode: \( \boldsymbol{\text{No Mode}} \), Range: \( \boldsymbol{17} \)

Problem 6

a. Range: \( \boldsymbol{17} \)
b. Mean: \( \boldsymbol{23.75} \), Median: \( \boldsymbol{23.50} \), Mode: \( \boldsymbol{\text{No Mode}} \)