After increasing each value in the data set by 25:
New Mean = 134
New Median = 129
New Mode = 121
New Range = 70
Standard Deviation remains unchanged at 3.6
Let's consider the effects of increasing each value in the data set by 25 on the measures:
Mean:
Mean is the sum of all values divided by the number of values.
Given: Mean = 109
When each value increases by 25, the new mean would increase by 25 as well.
New Mean = 109 + 25 = 134
Median:
Median is the middle value when the data set is arranged in ascending order.
Given: Median = 104
When each value increases by 25, the median would also increase by 25.
New Median = 104 + 25 = 129
Mode:
Mode is the most frequently occurring value in the data set.
Given: Mode = 96
When each value increases by 25, the mode would also increase by 25.
New Mode = 96 + 25 = 121
Range:
Range is the difference between the maximum and minimum values in the data set.
Given: Range = 45
Since every value in the data set increases by 25, the range would also increase by 25.
New Range = 45 + 25 = 70
Standard Deviation:
The standard deviation measures the amount of variation or dispersion in a set of values.
Given: Standard Deviation = 3.6
When every value increases by 25, the standard deviation remains unchanged because it measures the spread or variability of the values relative to the mean, not the individual values themselves.
So, after increasing each value in the data set by 25:
New Mean = 134
New Median = 129
New Mode = 121
New Range = 70
Standard Deviation remains unchanged at 3.6
Question
Find the values of the measures shown when each value in the data set increases by 25. Mean: 109 Median: 104 Mode: 96 Range: 45 Standard deviation: 3.6