This document contains 7 math problems involving statistical concepts like range, interquartile range, mean, variance, standard deviation, box plots, stem-and-leaf diagrams, and manipulating data sets. The problems cover finding measures of central tendency and dispersion for various data sets, comparing data visually using box plots, determining how changing data values affects statistical properties, and justifying which measures of dispersion to use for a given data set.

1. Name : Class :
1. Find the range for the ungrouped data below.
110, 120, 70, 200, 190, 120, 100
2. Find the interquartile range for each of the following sets of data.
a) 44, 55, 33, 35, 39, 40, 49, 50, 59, 40, 36
b)
3. Based on the ungrouped data provided, find the mean, variance, 𝜎2
and standard
deviation, 𝜎.
3.0, 3.1, 3.2, 3.4, 3.6, 3.7, 4.0, 4.1, 3.9
4. The box plot shows the scores obtained by two students in a test.
Determine which student
a) Has a greater median of test score
b) Has the greater interquartile range of test scores
c) Has the greater range of test scores
x 1 2 3 4 5 6
f 3 4 6 5 1 1

2. 5. The interquartile range and the standard deviation of a set of data are 6 and 1.414
respectively. Each number in the set of the data is multiplied by 5 and then 2 is deducted
from it.
Calculate the new value of
a) Interquartile range
b) Variance, 𝜎2
c) Standard deviation, 𝜎
6. The stem-and-leaf diagram shows a survey done among 20 pupils to find the number of
times they logged on to Google Classroom account
Which measures of dispersion is suitable to represent the number of times students
logged on to Google Classroom account over the past two months? Justify your answer.
7. A set of data consists of 10 numbers has the mean of 8 and the standard deviation of 1.2.
a) Find
i. Σ𝑥
ii. Σ𝑥2
b) Each data is divided by 4 and then 3 is added to it. Find
i. The new mean
ii. The new variance.