Selina solutions

# Question 1

Q1) Find the median of (i) 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25 (ii) 3.2, 4.8, 5.6, 5.6, 7.3, 8.9 and 9.1 (iii) 17, 23, 36, 12, 18, 23, 40 and 20 (iv) 26, 33, 41, 18, 30, 22, 36, 45 and 24 (v) 80, 48, 66, 61, 75, 52, 45 and 70

Solution 1:

(i) Observations = 21, 21, 22, 23, 23, 24, 24, 24, 24, 25, 25

No. of terms = 11

Middle term = 6th term = 24

(ii) Observations = 3.2, 4.8, 5.6, 5.6, 7.3, 8.9, 9.1

No. of terms = 7

Middle term = 4th term = 5.6

(iii) Observations = 12, 17, 18, 20, 23, 23, 36, 40

No. of terms = 8 (even)

Median = \frac{1}{2}\left\{\frac{n}{2}th\ term\ +\ \left(\frac{n}{2}+1\right)th\ term\right\}

= \frac{1}{2}\left\{\frac{8}{2}th+\left(\frac{8}{2}+1\right)th\ \right\}=\frac{1}{2}\left\{4th\ term\ +\ 5th\ term\right\}

= \frac{1}{2}\left(20+23\right)=\frac{43}{2}=21.5

(iv) Observations = 18, 22, 24, 26, 30, 33, 36, 41, 45

No. of terms = 9 (odd)

Median = \left(\frac{n+1}{2}\right)th\ term

= \frac{9+1}{2}=\frac{10}{2}=5th\ term = 30

(v) Observations = 45, 48, 52, 61, 66, 70, 75, 80

No. of terms = 8 (even)

Median = \frac{1}{2}\left\{\frac{n}{2}th\ term\ +\ \left(\frac{n}{2}+1\right)th\ term\right\}

= \frac{1}{2}\left\{\frac{8}{2}th+\left(\frac{8}{2}+1\right)th\ \right\}=\frac{1}{2}\left\{4th\ term\ +\ 5th\ term\right\}

= \frac{1}{2}\left(61+66\right)=\frac{127}{2}=63.5

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