Height (cm) Number of persons 120 3 130 4 140 5 150 6 160 2
Calculate Mean Height from Frequency Data
To determine the mean height from the provided frequency distribution data, we follow a standard calculation method. This involves multiplying each height value by its corresponding frequency (number of persons), summing these products, and then dividing by the total number of persons.
| Height (cm) | Number of persons (f) | fx |
| 120 | 3 | 360 |
| 130 | 4 | 520 |
| 140 | 5 | 700 |
| 150 | 6 | 900 |
| 160 | 2 | 320 |
| Total | $ \sum f = 20 $ | $ \sum fx = 2800 $ |
Mean Height Calculation Steps
- Multiply Height by Frequency: Calculate the product ($fx$) for each row by multiplying the height ($x$) by the number of persons ($f$).
-
Sum the Products: Obtain the total sum of the $fx$ column ($ \sum fx $).
$ \sum fx = 360 + 520 + 700 + 900 + 320 = 2800 $ -
Sum the Frequencies: Obtain the total sum of the 'Number of persons' column ($ \sum f $).
$ \sum f = 3 + 4 + 5 + 6 + 2 = 20 $ -
Calculate the Mean: Divide the total sum of products ($ \sum fx $) by the total frequency ($ \sum f $).
Mean height = $ \frac{\sum fx}{\sum f} $
Mean height = $ \frac{2800}{20} $
Mean height = $ 140 $ cm
The mean height calculated from the data is 140 cm.
Similar Questions
- Let a set S = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Then the value of $4 \times \text{mean} + 2 \times \text{mode} - 8 \times \text{median}$ is:
- The weights (in kg) of 7 men are 64, 63, 62, 65, 67, 66 and 61. The median weight is:
- Which of the following CANNOT take a negative value?
- The given data is arranged in ascending order and its median is 17. Find the value of $x$.
$8, 10, 12, 15, x, x + 2, 20, 25, 30, 32$ - Find the sum of the mean, median and mode of the given data.
$9, 35, 20, 25, 25, 15, 25$ - In the given data if 30 is replaced by 100 then find the difference of the two medians.
80, 90, 40, 30, 20, 10, 70, 60, 50 - If the mean of the following data is k, then find the value of k.
Value 3 2 k 4 5 Frequency k 2k 3k 4k 5k - A alone can complete a work in 12 days and B alone can complete the same work in 18 days. They started working together, but A left after 3 days. In how many days will B alone be able to complete the remaining work?
- For the data set 1, 2, 3, 5, 2, 3, 4, 6, 6, 8, 3, 4, 5 which of the following options is INCORRECT?
- If the median and mean are 36 and 35 respectively, find the mode.
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
