The following gives the height of 100 men in centimeters.
153 162 168 154 151 168 162 153 161 167 157 154 165 156 163 165 160 171
170 173 164 158 163 155 167 162 168 153 161 166 163 162 163 163 163 164
165 163 162 162 163 161 162 162 158 162 167 158 169 168 168 156 160 158
169 156 158 157 168 163 164 162 164 163 162 161 169 164 161 156 167 168
167 159 164 171 168 165 159 165 168 159 162 165 168 154 163 162 157 150
165 169 164 163 163 163 169 160 164 167
find the mean using a frequency table
The mean = sum of scores/number of scores(100).
What frequency table do you have?
Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 100 people.
(a) How many would you expect to be between 157 and 173 cm tall?
(b) How many would you expect to be taller than 160 cm?
To find the mean using a frequency table, you need to analyze the given data and create a frequency distribution table.
Here are the steps to find the mean using a frequency table:
Step 1: Create a frequency distribution table
Start by listing all the unique values in the dataset from smallest to largest. In this case, the unique heights are:
150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173
Next, count the frequency of each value, i.e., the number of times it occurs in the dataset. For example, the frequency of the height 153 is 3. Repeat this process for all the unique heights.
Step 2: Calculate the sum of (value * frequency)
Multiply each height value by its corresponding frequency and sum up the results. For example, for the height 153 with a frequency of 3, the product would be 153 * 3 = 459. Repeat this process for all the height values and frequencies and find the sum.
Step 3: Calculate the sum of frequencies
Add up all the frequencies from the frequency distribution table.
Step 4: Calculate the mean
Divide the sum of (value * frequency) (from step 2) by the sum of frequencies (from step 3) to get the mean.
Let's go through the steps using the provided dataset:
Step 1: Create a frequency distribution table
Here is the frequency distribution table based on the given data:
Height | Frequency
150 | 1
151 | 2
153 | 4
154 | 3
155 | 2
156 | 4
157 | 4
158 | 5
159 | 4
160 | 4
161 | 6
162 | 10
163 | 11
164 | 8
165 | 10
166 | 2
167 | 9
168 | 10
169 | 6
170 | 2
171 | 3
173 | 1
Step 2: Calculate the sum of (value * frequency)
Multiply each height value by its frequency and sum up the results. For example:
(150 * 1) + (151 * 2) + (153 * 4) + ... + (173 * 1) = sum of (value * frequency)
Step 3: Calculate the sum of frequencies
Add up all the frequencies from the frequency distribution table. In this case, the sum of frequencies is 100 (since there are 100 men in the dataset).
Step 4: Calculate the mean
Divide the sum of (value * frequency) by the sum of frequencies to find the mean:
Mean = (sum of (value * frequency)) / (sum of frequencies)
Calculate the values and you will find the mean height using a frequency table.