Objective: Students
will be able to analyze a frequency distribution using
statistics.
Frequency distribution is a summary of raw data that
displays the data elements according to frequency of
occurrence. It can be represented by either a table or a
histogram.
Numbers that are applied to analyze frequency distribution are
called statistics. Some of these numbers are mean, median,
mode, and range.
Mean(arithmetic mean or average) is the sum of the data
in a frequency distribution divided by the number of data
elements.
Median is the value of the middle element when the
sample size is odd (or the average value of the two middle
elements when the sample size is even) in a frequency
distribution. To find the median, the data elements must be in
order.
Mode is the most frequently occurring value in a
frequency distribution.
Range is the difference between the highest and the
lowest values in a frequency distribution.
Example: Three dice are rolled 12 times. The sum of the
numbers after each roll is recorded in the following table.
| Roll |
Sum |
| 1 |
12 |
| 2 |
11 |
| 3 |
4 |
| 4 |
3 |
| 5 |
12 |
| 6 |
17 |
| 7 |
8 |
| 8 |
12 |
| 9 |
7 |
| 10 |
5 |
| 11 |
13 |
| 12 |
4 |
Find the mean, median, mode, and range of the data in the
above table.
Answer:
Step 1: Rearrange the data elements.
3, 4, 4, 5, 7, 8, 11, 12 ,12, 12, 13, 17
Step 2: Find the mean.
Step 3: Find the median.
The sample size is even, for there are 12 data elements.
The median is the average value of the sixth and the seventh
elements.
median = (8+11)/2 = 9.5
Step 4: Find the mode.
The number 3 occurs once.
The number 4 occurs twice.
The number 5 occurs once.
The number 7 occurs once.
The number 8 occurs once.
The number 11 occurs once.
The number 12 occurs three times.
The number 13 occurs once.
The number 17 occurs once.
mode = 12
Step 5: Find the range.
The highest value is 17.
The lowest value is 3.
range = 17-3 = 14
Example: The multiple-choice test scores of the
students in Mr. Smith's chemistry class are recorded in the
following histogram.
Find the mean, median, mode, and range of the data in the
above histogram.
Answer:
Step 1: Rearrange the data elements.
64, 64, 68, 72, 72, 72, 72, 72, 76, 76, 76, 76, 80, 80, 80,
80, 80, 80, 80, 84, 84, 84, 84, 84, 84, 84, 88, 88, 88, 88,
88, 88, 88, 88, 88, 92, 92, 92, 92, 92, 92, 92, 96, 96, 96,
100
Step 2: Find the mean.
Step 3: Find the median.
The sample size is even, for there are 46 data elements.
The median is the average value of the twenty-third and the
twenty-fourth elements.
median = (84+84)/2 = 84
Step 4: Find the mode.
The score 64 occurs twice.
The score 68 occurs once.
The score 72 occurs five times.
The score 76 occurs four times.
The score 80 occurs seven times.
The score 84 occurs seven times.
The score 88 occurs nine times.
The score 92 occurs seven times.
The score 96 occurs three times.
The score 100 occurs once.
mode = 88
Step 5: Find the range.
The highest value is 100.
The lowest value is 64.
range = 100 - 64 = 36
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