Concept explainers
To calculate mean, median, mode, rangeand standard deviation after multiplying the given constant.
Answer to Problem 11PPS
Mean is 36.8.
Median is 38.
Mode is 12.
Standard deviation is 19.98
Range is56
Explanation of Solution
Given information:
Frequency: 11,7,3,13,16,8,3,11,17,3
Constant to be multiplied: 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,
Multiply 4 to all the frequency values,
New frequency:
44,28,12,52,64,32,12,44,68,12
Sorting the frequency
12,12,12,28,32,44,44,52,64,68
For Mean,
Substituting the values in mean formula,
On solving,
Hence, Mean is 36.8.
For median,
Substituting values,
On solving,
Substituting the values,
On solving,
Hence, Median is 38.
For mode,
Mode is the item with the maximum frequency, which is 12.
For standard deviation,
Substituting the values in standard deviation formula,
On solving,
So,
On solving,
Hence, Standard deviation is 19.98
For Range,
Substituting in the range formula,
On solving,
Chapter 10 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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