This is a statistics problem involving Group Frequency Distribution Table. See the attached and the details below.
What is a Group Frequency Distribution Table?
By dividing observations into intervals and tabulating the frequencies for each interval, data can be organized. A grouped frequency table is the end product.
The intervals in this distribution are referred to as classes.
What is the Estimated Mean of the Grouped Frequencies?
This is obtained by dividing the sum of the product of all mid points and their frequencies by the total number of observations.
That is Estimated Mean = (f * x)/n ------See the attached sheet.
⇒ 503/50
= 10.06
What is the Estimated Median of the Grouped Frequencies?
The median of the 50 observations = 28
This is arrived at by dividing the sum of 25th and the 26th number by 2.
That is (28 + 28)/28=28
This median falls in to the third class - 25-29. Hence, the median group is 25-29.
The estimated median value is computed as follows:
Estimated Median = L + (((n/2)-B)/G) x w
Where :
- L is the lower class boundary of the group containing the median
- n is the total number of values
- B is the cumulative frequency of the groups before the median group
- G is the frequency of the median group
- w is the group width
Inserting the values we have :
L = 25
n = 50
B = 0 + 1 = 1
G = 2
w = 5
Estimated Median = 25 + (((50/2)-1)/2 ) * 5
= 25 + (24/2) * 5
= 85
How do you calculate the Estimated Mode?
By observation, the modal group is 30-34. This is because it has the highest frequency of 4.
Hence, the Estimated Mode (EM) is arrived at using the formula:
EM = L + (fₙ-fₙ₋₁)/(fₙ-fₙ₋₁) + (fₙ-fₙ₊₁) x w
where:
- L is the lower class boundary of the modal group
- fn-1 is the frequency of the group before the modal group
- fn is the frequency of the modal group
- fn+1 is the frequency of the group after the modal group
- w is the group width
Note that
L = 30
fn-1 = 2
fn = 4
fn+1 = 3
w = 5
Hence,
EM = 30 + (4-2)/((4-2) + (4-3)) x 5
= 30 + (2/(2+1)) x 5
= 30 + (2/3) x 5
EM = 33.33
In summary,
- Estimated Mean: 10.06
- Estimated Median: 85
- Estimated Mode: 33.33
Learn more about Group Frequency Distribution at:
https://brainly.com/question/11228919
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