Question

Arithmetic mean of 56, 57, 58, ...., 100 is:​

Answer 1

$\tt{ \underline{✪ \: Qᴜᴇsᴛɪᴏɴ : ✪}}$

→ Arithmetic Mean of 56, 57, 58, ........, 100 is:

$\tt{ \underline{✪ \: ᴀɴsᴡᴇʀ : ✪}}$

$\tt \pink{→ Arithmetic \: Mean = \frac{Sum \: of \: observations}{Total \: no. \: of \: observation}}$

$\tt \pink{→ Sum \: of \: first \: “n” \: natural \: number = \frac{n(n+1)}{2}}$

$\tt \pink{→ Sum \: of \: first \: “100” \: natural \: number = \frac{100 \times 101}{2} = 5050}$

$\tt \pink{→ Sum \: of \: first \: “50” \: natural \: number = \frac{55 \times 56}{2} = 1540}$

$\tt \pink{→ Sum \: of \: 56, 57, 58, ...., 100 = 5050 - 1540}$

$\tt \pink{→ 3510}$

$\tt \pink{→ Arithmetic \: \: Mean = \frac{3510}{45} = 78}$