Concept explainers
To calculate mean, median, mode, rangeand standard deviation after adding the given constant.
Answer to Problem 2CYU
Mean is 60.75.
Median is 60.5.
Mode is 65.
Standard deviation is 5.26.
Range is 16
Explanation of Solution
Given information:
Frequency: 38,36,37,42,31,44,37,45,29,42,30,42
Constant to be added: +23
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,
Add 23 to all the frequency values,
New frequency:
61,59,60,65,54,67,60,68,52,65,53,65
For Mean,
Substituting the values in mean formula,
So,
On solving,
Hence, Mean is 60.75
For median,
Sorting the frequency
52,53,54,59,60,60,61,65,65,65,67,68
Substituting values,
On solving,
Substituting the values,
On solving,
Hence, Median is 60.5.
For mode,
Mode is the item with the maximum frequency. Substituting the values,
For standard deviation,
Substituting the values in standard deviation formula,
So,
On solving,
On solving,
Hence, Standard deviation is 5.26
For Range,
Range is the difference between the lowest and highest values.
Substituting the values,
On solving,
Chapter 10 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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