Question 14iii 50 students enter for a school javelin throw competition- The distance in metres thrown are recorded below - - - - - 0-20 20-40 40-60 60-80 80-100- - - - 6 11 17 12 4- - Calculate the median distance by using the formula for the median-

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Standard VII

Mathematics

Introduction to Statistics

Question 14ii...

Question

Question 14(iii)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

Calculate the median distance by using the formula for the median.

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Solution

Now, $\frac{N}{2} = \frac{50}{2} = 25$
which lies in the inteval 40-60.
$∴$ l=40, h=20, cf=17 and f=17
$∴ M e d i a n = l + (\frac{\frac{N}{2} - c f}{f}) \times h = 40 + \frac{(25 - 17)}{17} \times 20 = 40 + \frac{8 \times 20}{17} = 40 + 9.41 = 49.41$

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Question 14(iv)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

Are the median distance calculated in (ii) and (iii) same?

Question 14(ii)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

(ii) Draw a cumulative frequency curve (less than type) and calculate the median distance thrown by using this curve.

Question 14(i)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

Construct a cumulative frequency table.

Question 14(iii)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

Calculate the median distance by using the formula for the median.

Question 14(iv)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{matrix} D i s t a n c e (i n m) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 N u m b e r o f s t u d e n t s & 6 & 11 & 17 & 12 & 4 \end{matrix}$

Are the median distance calculated in (ii) and (iii) same?

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Question 14(iii) 50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below : Distance (in m)0−2020−4040−6060−8080−100Number of students 6 11 17 12 4 Calculate the median distance by using the formula for the median.

Now, N2=502=25 which lies in the inteval 40-60. ∴ l=40, h=20, cf=17 and f=17 ∴Median=l+(N2−cff)×h =40+(25−17)17×20 =40+8×2017 =40+9.41 =49.41

Now, $\frac{N}{2} = \frac{50}{2} = 25$
which lies in the inteval 40-60.
$∴$ l=40, h=20, cf=17 and f=17
$∴ M e d i a n = l + (\frac{\frac{N}{2} - c f}{f}) \times h = 40 + \frac{(25 - 17)}{17} \times 20 = 40 + \frac{8 \times 20}{17} = 40 + 9.41 = 49.41$