
Concept explainers
To calculate mean, median, mode, rangeand standard deviation after adding the given constant.

Answer to Problem 9PPS
Mean is 22.5.
Median is 21.5.
Mode is 17.
Standard deviation is 7.36
Range is 24
Explanation of Solution
Given information:
Frequency: 27,21,34,42,20,19,18,26,25,33
Constant to be added: -4
Formula used:Mean formula is,
Where, f is frequency
N is total number of items
X is item.
Median formula is,
, where N cumulative frequency
Mode is the item with the maximum frequency.
Standard deviation is,
Where, SD= standard deviation,
x = value
Calculation:
According to question,
Add -4 to all the frequency values,
New frequency:
23,17,30,38,16,15,14,22,21,29
Sorting the frequency
14,15,16,17,21,22,23,29,30,38
For Mean,
Substituting the values in mean formula,
So,
On solving,
Hence, Mean is 22.5
For median,
Substituting values,
On solving,
Substituting the values,
On solving,
Hence, Median is 21.5.
For mode,
Grouping frequencies into classes of interval 5.
15-19: 4
20-24:3
25-29:1
30-34:1
35-39:1
“15-19” appear most often, so mode is 17
For standard deviation,
Substituting the values in standard deviation formula,
On solving,
On solving,
Hence, Standard deviation is 7.76
For Range,
Substituting in the range formula,
On solving,
Hence, range is 24
Chapter 10 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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