Question

Students of class X of a school decided to donate their pocket money to purchase food packets for
people who suffer from this lock down due to Covid - 19. They packed the food packets in different boxes. These
boxes contained varying number of food packets. The following was the distribution of food packets according to the
number of boxes.
No. of Food packet 50-52 53-55 56-58 59-61 62-64
No. of boxes 15 110 135 115 25
(a) Find the mean number of food packets kept in a packing box.
(b) Draw cumulative frequency curve on graph sheet(less than type & more than type) and calculate the median
number of food packets kept in a packing box.
(c) Calculate the median number of food packets kept in a packing box by using formula.
(d) Are the median calculated in (b) and (c) same?
(e) Calculate the mode number of food packets kept in a packing box by using formula.

Answer 1

Given : distribution of food packets according to the  number of boxes.

To Find : mean number of food packets

median number of food packets

mode number of food packets

Draw cumulative frequency curve on graph sheet(less than type & more than type) and calculate the median number of food packets kept in a packing box.

Compare the median calculated by formula and graph

Solution:

Interval          Mean    f        cf     cf         d=(mean - 57)/3    df

49.5 - 52.5     51        15      15     400        - 2                        -30

52.5 - 55.5     54      110     125    385        -1                         -110

55.5 - 58.5     57      135     260   275        0                          0

58.5 - 61.5     60      115      375    140        1                          115

61.5 - 64.5     63      25     400     25          2                         50

                               400                                                        25

Mean = 57  +  3 x 25/400

= 57 + 0.1875

= 57.1875

≈ 57.2

Median = 55.5 + 3 x (200 - 125)/135

= 55.5 + 1.67

= 57.17

≈ 57.2

Mode = 55.5 + 3 x ( 135 - 110)/(135 - 110 + 135 - 115)

= 55.5 + 1.67

= 57.17

≈ 57.2

From Graph Median ≈ 57.2

(Same as by Formula )

Less than ogive

The points with the upper limits of the class are plotted on x axis  and the corresponding less than cumulative frequencies on y axis.

More than ogive

The points with the Lower limits of the class are plotted on x axis  and the corresponding more than cumulative frequencies on y axis.

Learn More:

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