Concept explainers
To calculate mean, median, mode, rangeand standard deviation after multiplying the given constant.
Answer to Problem 13PPS
Mean is 28.6.
Median is 27.2.
Mode is 29.6.
Standard deviation is 3.47
Range is10.4
Explanation of Solution
Given information:
Frequency: 33,37,38,29,35,37,27,40,28,31
Constant to be multiplied= 0.8
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
The Range is the difference between the lowest and highest values.
Calculation:
According to question,
Multiplying 0.8 to all the frequency values,
New frequency:
26.4,29.6,30.4,23.2,28,29.6,21.6,32,22.4,24.8
Sorting the frequency
21.6, 22.4, 23.2, 24.8, 26.4, 28, 29.6, 29.6, 30.4,32
For Mean,
Substituting the values in mean formula,
So,
On solving,
Hence, Mean is 28.6
For median,
Substituting values,
On solving,
Substituting the values,
On solving,
Hence, Median is 27.2.
For mode,
Mode is the item with the maximum frequency which is 29.6.
For standard deviation,
Substituting values,
So,
On solving,
Hence, Standard deviation is 3.473
For Range,
Range is the difference between the lowest and highest values.
Substituting values,
On solving,
Hence, range is 10.4
Chapter 10 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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