Find the mean of the following data
class. frequency intarval.
0-9. 5
10-19. 9
20-29. 12
30-39. 24
40-49. 17
can u send these answer before 18 August 2020
50-59. 3.
Answers
hope it helps ☺️
hope it helps ☺️
Answer:
The mean of the given data is 7.19 (approx.).
Step-by-step-explanation:
We have given a frequency distribution.
We have to find mean of the given data.
___________________________
Class interval ∣ Frequency
___________________________
0 - 9 .............. ∣............. 5
___________________________
10 - 19 .......... ∣........... 9
___________________________
20 - 29 ........ ∣............ 12
___________________________
30 - 39 ......... ∣.......... 24
___________________________
40 - 49 ...... ∣ .......... 17
___________________________
50 - 59 ..... ∣........... 3
___________________________
Here, the classes are not continuous.
The difference between the upper class limit of a class and the lower class limit of its succeeding class is -
⇒ 10 - 9 = 1
∴ 1 ÷ 2 = 0.5
Subtract 0.5 from the lower class limit of each class.
And add 0.5 to the upper class limit of each class.
_________________________________
Class ∣ Continuous ∣ Class ∣ Frequency ∣ xᵢ.fᵢ
interval | class | marks (xᵢ) | (fᵢ)
__________________________________
0 - 9 | - 0.5 - 9.5 | 4.5 | 5 | 22.5
__________________________________
10 - 19 | 9.5 - 19.5 | 5.5 | 9 | 49.5
___________________________________
20 - 29 | 19.5 - 29.5 | 6.5 | 12 | 78
___________________________________
30 - 39 | 29.5 - 39.5 | 7.5 | 24 | 180
___________________________________
40 - 49 | 39.5 - 49.5 | 8.5 | 17 | 144.5
___________________________________
50 - 59 | 49.5 - 59.5 | 9.5 | 3 | 28.5
___________________________________
Total | ___ | ____ | __ | Σfᵢ = 70 | Σxᵢfᵢ = 503
___________________________________
Now,
Mean X = Σxᵢfᵢ / Σfᵢ
⇒ Mean = 503 / 70
⇒ Mean = 7.185
⇒ Mean ≈ 7.19
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Additional Information:
1. Mean:
The mean means average of the given data.
2. It is calculated by the division of the total sum of all the scores and total number of scores.
3. Mean is denoted by X.
4. Mean of grouped-frequency distribution:
When the number of scores is large in amount, some different methods are used to calculate its mean.
There are three methods to calculate the mean of grouped - frequency distribution:
A. Direct Method
B. Assumed Mean Method
C. Step deviation method
5. Direct Method:
The division of the multiplication of class marks and frequency & sum of frequency mean mean by direct method.
6. Formula for Mean by Direct method:
Mean X = Σxᵢfᵢ / Σfᵢ