Advertisements
Advertisements
प्रश्न
The weights of tea in 70 packets are shown in the following table:
| Weight | 200 – 201 |
201 – 202 |
202 – 203 |
203 – 204 |
204 – 205 |
205 – 206 |
| Number of packets | 13 | 27 | 18 | 10 | 1 | 1 |
Find the mean weight of packets using step deviation method.
उत्तर
Let us choose a = 202.5, h = 1, then `d_i = x_i – 202.5 and u_i = (x_i-202.5)/1`
Using step-deviation method, the given data is shown as follows:
| Weight | Number of packets `(f_i)` |
Class mark `(x_i)` |
`d_i = x_i `–202.5 | `u_i = (x_i−202.5)/ 1` |
`(f_i u_i)` |
| 200 - 201 | 13 | 200.5 | -2 | -2 | -26 |
| 201 – 202 | 27 | 201.5 | -1 | -1 | -27 |
| 202 – 203 | 18 | 202.5 | 0 | 0 | 0 |
| 203 – 204 | 10 | 203.5 | 1 | 1 | 10 |
| 204 – 205 | 1 | 204.5 | 2 | 2 | 2 |
| 205 – 206 | 1 | 205.5 | 3 | 3 | 3 |
| Total | `Ʃ f_i` = 70 | `Ʃ f_i u_i `= -38 |
The mean of the given data is given by,
x =` a+ ((sum _i f_i u_i)/( sum _i f_i)) xxh`
=`202.5 + ((-38)/70) xx1`
=202.5 – 0.542
= 201.96
Hence, the mean is 201.96 g.
APPEARS IN
संबंधित प्रश्न
Find the missing value of p for the following distribution whose mean is 12.58
| x | 5 | 8 | 10 | 12 | P | 20 | 25 |
| f | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
The daily expenditure of 100 families are given below. Calculate `f_1` and `f_2` if the mean daily expenditure is ₹ 188.
|
Expenditure (in Rs) |
140-160 | 160-180 | 180-200 | 200-220 | 220-240 |
|
Number of families |
5 | 25 | `f_1` | `f_2` | 5 |
If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =
The measurements (in mm) of the diameters of the head of the screws are given below :
| Diameter (in mm) | no. of screws |
| 33 - 35 | 9 |
| 36 - 38 | 21 |
| 39 - 41 | 30 |
| 42 - 44 | 22 |
| 45 - 47 | 18 |
Calculate the mean diameter of the head of a screw by the ' Assumed Mean Method'.
The marks obtained by a set of students in an examination all given below:
| Marks | 5 | 10 | 15 | 20 | 25 | 30 |
| Number of students | 6 | 4 | 6 | 12 | x | 4 |
Given that the mean marks of the set of students is 18, Calculate the numerical value of x.
If the mean of n observation ax1, ax2, ax3,....,axn is a`bar"X"`, show that `(ax_1 - abar"X") + (ax_2 - abar"X") + ...(ax_"n" - abar"X")` = 0.
In the formula `barx = a + h((sumf_iu_i)/(sumf_i))`, for finding the mean of grouped frequency distribution, ui = ______.
Find the mean, median and mode of the given data:
| Class | 65 – 85 | 85 – 105 | 105 – 125 | 125 – 145 | 145 – 165 | 165 – 185 | 185 –205 |
| Frequency | 8 | 7 | 22 | 17 | 13 | 5 | 3 |
250 apples of a box were weighed and the distribution of masses of the apples is given in the following table:
| Mass (in grams) |
80 – 100 | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 |
| Number of apples |
20 | 60 | 70 | x | 60 |
Find the value of x and the mean mass of the apples.
The following table gives the distribution of the life time of 400 neon lamps:
| Life time (in hours) | Number of lamps |
| 1500 – 2000 | 14 |
| 2000 – 2500 | 56 |
| 2500 – 3000 | 60 |
| 3000 – 3500 | 86 |
| 3500 – 4000 | 74 |
| 4000 – 4500 | 62 |
| 4500 – 5000 | 48 |
Find the average life time of a lamp.
