Advertisements
Advertisements
प्रश्न
From the following data, draw the two types of cumulative frequency curves and determine the median:
| Marks | Frequency |
| 140 – 144 | 3 |
| 144 – 148 | 9 |
| 148 – 152 | 24 |
| 152 – 156 | 31 |
| 156 – 160 | 42 |
| 160 – 164 | 64 |
| 164 – 168 | 75 |
| 168 – 172 | 82 |
| 172 – 176 | 86 |
| 176 – 180 | 34 |
उत्तर
(i) Less than series:
| Marks | Number of students |
| Less than 144 | 3 |
| Less than 148 | 12 |
| Less than 152 | 36 |
| Less than 156 | 67 |
| Less than 160 | 109 |
| Less than 164 | 173 |
| Less than 168 | 248 |
| Less than 172 | 230 |
| Less than 176 | 416 |
| Less than 180 | 450 |
We plot the points A(144, 3), B(148, 12), C(152, 36), D(156, 67), E(160, 109), F(164, 173), G(168, 248) and H(172, 330), I(176, 416) and J(180, 450).
Join AB, BC, CD, DE, EF, FG, GH, HI, IJ and JA with a free hand to get the curve representing the ‘less than type’ series.
(ii) More than series:
| Marks | Number of students |
| More than 140 | 450 |
| More than 144 | 447 |
| More than 148 | 438 |
| More than 152 | 414 |
| More than 156 | 383 |
| More than 160 | 341 |
| More than 164 | 277 |
| More than 168 | 202 |
| More than 172 | 120 |
| More than 176 | 34 |
Now, on the same graph paper, we plot the points A1(140, 450), B1(144, 447), C1(148, 438), D1(152, 414), E1(156, 383), F1(160, 277), H1(168, 202), I1(172, 120) and J1(176, 34).
Join A1B1, B1C1, C1D1, D1E1, E1F1, F1G1, G1H1, H1I1 and I1J1 with a free hand to get the ‘more than type’ series.
The two curves intersect at point L. Draw LM ⊥ OX cutting the x-axis at M. Clearly, M = 166cm
Hence, median = 166cm
APPEARS IN
संबंधित प्रश्न
The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:
| Monthly Consumption (in units) | 140 – 160 | 160 – 180 | 180 – 200 | 200 – 220 | 220 – 240 | 240 – 260 | 260 - 280 |
| Number of Families | 3 | 8 | 15 | 40 | 50 | 30 | 10 |
Prepare a ‘more than type’ ogive for the given frequency distribution.
The monthly pocket money of 50 students of a class are given in the following distribution
| Monthly pocket money (in Rs) | 0 - 50 | 50 – 100 | 100 – 150 | 150 -200 | 200 – 250 | 250 - 300 |
| Number of Students | 2 | 7 | 8 | 30 | 12 | 1 |
Find the modal class and give class mark of the modal class.
What is the cumulative frequency of the modal class of the following distribution?
| Class | 3 – 6 | 6 – 9 | 9 – 12 | 12 – 15 | 15 – 18 | 18 – 21 | 21 – 24 |
|
Frequency |
7 | 13 | 10 | 23 | 54 | 21 | 16 |
Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24
| Age (in years) | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Number of persons |
5 | 25 | ? | 18 | 7 |
Write the modal class for the following frequency distribution:
| Class-interval: | 10−15 | 15−20 | 20−25 | 25−30 | 30−35 | 35−40 |
| Frequency: | 30 | 35 | 75 | 40 | 30 | 15 |
If \[u_i = \frac{x_i - 25}{10}, \Sigma f_i u_i = 20, \Sigma f_i = 100, \text { then }\]`overlineX`
If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.
If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | Total |
| Frequency | f1 | 5 | 9 | 12 | f2 | 3 | 2 | 40 |
For one term, absentee record of students is given below. If mean is 15.5, then the missing frequencies x and y are.
| Number of days | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | TOTAL |
| Total Number of students | 15 | 16 | x | 8 | y | 8 | 6 | 4 | 70 |
The following is the distribution of weights (in kg) of 40 persons:
| Weight (in kg) | 40 – 45 | 45 – 50 | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 | 70 – 75 | 75 – 80 |
| Number of persons | 4 | 4 | 13 | 5 | 6 | 5 | 2 | 1 |
Construct a cumulative frequency distribution (of the less than type) table for the data above.
