We know to find the mean, median, and mode of the data set shown in the stem-and-leaf plot. Let's start by looking at the given diagram!
Ages of Office Workers
rrr|l
& &Steam & Leaf [0.15em]
[-0.75em]
& &2 & 3 5 8 8
& &3 & 1 2 3 3 6 9
& &4 & 2 5 7
& &5 & 1 3
2|3=23 years
The given stem-and-leaf plot was constructed by breaking each number from the data set into a stem and a leaf.
r|c
2_(stem) & 3_(leaf)
With this information, we can write a list of all data values.
23, 25, 28, 28, 31, 32, 33, 33, 36, 39, 42, 45, 47, 51, 53
We will calculate each measure of center separately.
Mean
The mean of a set of data values is the sum of all the values divided by the number of values.
Mean = Sum of values/Number of values
Let's start by adding the values from the data set.
23+25+28+28+31+32+33+33 + 36+39+42+45+47+51+53 = 546
We can see that the sum of 15 values in the data set is equal to 546. Let's substitute the sum, as well as the number of values, into the formula for the mean.
&Mean = 546/15 [0.8em] &Mean= 36.4
The mean of the data set is approximately 36.4.
Median
A median of a data set is the middle number of an ordered set of data. Since our data set consists of 15 values, the middle number is the 8^(th) one.
23, 25, 28, 28, 31, 32, 33, 33, 36, 39, 42, 45, 47, 51, 53
This means that the median of the data set equals 33.
Mode
The mode of a data set is the value that occurs most frequently.
23, 25, 28, 28, 31, 32, 33, 33, 36, 39, 42, 45, 47, 51, 53
We can see that 28 and 33 occur more frequently than the other values, so there are two modes in this data set.
