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Measures of Spread - Worksheet 9 - 9th Grade

Hard

Calculate range, IQR, and standard deviation (Hard)

27 problems · 20-25 minutes · Skills: statistics, variability, data analysis

About This Worksheet

This hard-level worksheet contains 27 problems designed for 9th Grade students practicing measures of spread. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Spread tells you how consistent or variable a data set is — information the center alone cannot provide. Standard deviation in particular is one of the most widely used statistics in science, finance, and quality control, making it an important concept for any quantitative career.

  • Calculate range as the difference between the maximum and minimum
  • Find quartiles and compute the interquartile range (IQR)
  • Calculate and interpret standard deviation as the average distance from the mean
  • Identify outliers using the IQR rule (below Q1 minus 1.5 IQR or above Q3 plus 1.5 IQR)
  • Compare the spread of two data sets using their standard deviations

How to Solve: Worked Example

Example Problem: Find the mean and population variance of: 13, 15, 17, 19, 21
Solution Steps:
  1. Mean: (13 + 15 + 17 + 19 + 21)/5 = 85/5 = 17.
  2. Find each deviation from the mean: -4, -2, 0, 2, 4.
  3. Square them: 16, 4, 0, 4, 16, which sum to 40.
  4. Divide by the count: 40/5 = 8.
Answer: mean 17, variance 8
Tip: Squaring the deviations stops the positives and negatives cancelling to zero.
1
Find the mean and population variance: 15, 16, 17, 18, 19
2
Find the mean and population variance: -3, 1, 5, 9, 13
3
Find the mean and population variance: 10, 14, 18, 22, 26
4
Find the mean and population variance: 3, 6, 9, 12, 15
5
Find the mean and population variance: 8, 9, 10, 11, 12
6
Find the mean and population variance: 11, 12, 13, 14, 15
7
Find the mean and population variance: 1, 3, 5, 7, 9
8
Find the mean and population variance: 9, 11, 13, 15, 17
9
Find the mean and population variance: 7, 11, 15, 19, 23
10
Find the mean and population variance: 0, 2, 4, 6, 8
11
Find the mean and population variance: -1, 3, 7, 11, 15
12
Find the mean and population variance: 6, 8, 10, 12, 14
13
Find the mean and population variance: 12, 15, 18, 21, 24
14
Find the mean and population variance: 9, 12, 15, 18, 21
15
Find the mean and population variance: -4, 0, 4, 8, 12
16
Find the mean and population variance: 11, 13, 15, 17, 19
17
Find the mean and population variance: 15, 17, 19, 21, 23
18
Find the mean and population variance: 13, 15, 17, 19, 21
19
Find the mean and population variance: 17, 18, 19, 20, 21
20
Find the mean and population variance: -2, 2, 6, 10, 14
21
Find the mean and population variance: 6, 7, 8, 9, 10
22
Find the mean and population variance: 15, 16, 17, 18, 19
23
Find the mean and population variance: 5, 7, 9, 11, 13
24
Find the mean and population variance: 12, 15, 18, 21, 24
25
Find the mean and population variance: 3, 4, 5, 6, 7
26
Find the mean and population variance: 14, 16, 18, 20, 22
27
Find the mean and population variance: 18, 19, 20, 21, 22

Answer Key

1. mean 17, variance 22. mean 5, variance 323. mean 18, variance 324. mean 9, variance 185. mean 10, variance 26. mean 13, variance 27. mean 5, variance 88. mean 13, variance 89. mean 15, variance 3210. mean 4, variance 811. mean 7, variance 3212. mean 10, variance 813. mean 18, variance 1814. mean 15, variance 1815. mean 4, variance 3216. mean 15, variance 817. mean 19, variance 818. mean 17, variance 819. mean 19, variance 220. mean 6, variance 3221. mean 8, variance 222. mean 17, variance 223. mean 9, variance 824. mean 18, variance 1825. mean 5, variance 226. mean 18, variance 827. mean 20, variance 2

Frequently Asked Questions

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What skills does this statistics worksheet cover?

This worksheet focuses on statistics, variability, data analysis. It is designed for 9th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.