Question

Data of height of class 10th students was collected and organized as the following frequency distribution table; observe the median class and modal class.
Height (in cm)140-145 145-150 150-155 155-160 160-165 165-170 Frequency5 15 25 30 15 10
(i) What is the upper limit of the median class?(a) 150 cm (b) 160 cm (c) 155 cm (d) 165 cm(ii) What is the value of median height?(a)145.67 cm (b) 157.67 cm (c) 155.83 cm (d) 159.67 cm(iii) What is the lower limit of modal class? (a)150 cm (b) 160 cm (c) 155 cm (d) 165 cm(iv). What is the value of modal height?(a) 155.25 cm (b) 156.25 cm (c) 157.25 cm (d) 159.25 cm(v) What is the value of mean height?(a) 155.625 cm (b) 156.250 cm (c) 158.500 cm (d) 159.275 cm

Answer 1

Answer:

Step-by-step explanation:

There are 60 boys.  

To find the median height, we first arrange the class into increasing order of heights and then pick the height of the middle student as the median height.  

To find that on the ogive plot, we have to find the mark on the y-axis which corresponds to 30 boys and that would be the point 6 on the y-axis.  

Thus, the point on the x-axis which corresponds to the point 6 on the y-axis is the median height.  

We find that the number 6 on the y-axis corresponds to somewhere between 29 and 30 on the x-axis.  

That means, the median height range is 145−150cm.  

This is shown on the graph attached.

Answer 2

Given :  

Height (in cm)140-145 145-150 150-155 155-160 160-165 165-170

  Frequency         5             15         25           30         15            10

To Find :  value of median height

(a) 145.67 cm

(b) 157.67 cm

(c) 155.83 cm

(d) 159.67 cm

Step-by-step explanation:

Height (in cm)    F           CF     d = (mean - 157.5)/5    df

140-145              5            5           -3                             -15

145-150            15           20         -2                             -30

150-155            25          45         -1                             -25

155-160            30          75          0                              0

160-165            15           90          1                             15

165-170             10           100        2                            20

                        100                                                      - 35

100/2 = 50

upper limit of the median class 160

Median = 155 + 5  x ( 50 - 45)/30

= 155 + 0.83

=  155.83

value of median height  155.83 cm

MAX F = 30

lower limit of modal class 155

Mode =  155 + 5 ( 30 - 25)/(30 - 25 + 30 - 15)

= 155 +  25/ 20

=155 + 1.25

= 156.25

mean height  =  157.5 + 5 x (-35)/100

= 157.5 - 1.75

= 155.75 cm

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