Question

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes (in hours): 0-20 20-40 40-60 60-80 80-100 100-120
No of components: 10 35 52 61 38 29
Determine the modal lifetimes of the components​

Answer 1

Answer:

the modal lifetimes of the components is 65.625 hours.

Hope it helps you!

Answer 2

$\purple\dashrightarrow\tt{Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\hline\begin{array}{ ||c||c|| } \footnotesize \tt \underline{ \underline{ C.I}}& \footnotesize \tt\underline{ \underline{Frequency (fi)}}\\\footnotesize \tt{0-20}&\footnotesize \tt{10}\\\footnotesize \tt{20-40}&\footnotesize \tt{35}\\\footnotesize \tt{40-60}&\footnotesize \tt{52\dashrightarrow \: f0}\\\footnotesize \tt{l\dashleftarrow \:60-80}&\footnotesize \tt{61 \dashrightarrow \: f1}\\\footnotesize \tt{80-100}&\footnotesize \tt{38\dashrightarrow \: f2}\\\footnotesize \tt\underline{ \underline{100-120}}&\footnotesize \tt{\underline{ \underline{29}}}\end{array}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple\dashrightarrow \footnotesize\tt{Median(z) = l \: + \: } \tt{ \frac{f1 \: - \: f0}{2 \: f1 \: - \: f0 \: - \: f2} \times } \tt{ \: h}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \frac{61 \: - \: 52}{2 \: \times 61 \: - \: 52 \: - \: 38} \times } \tt{ \: 20}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \frac{9}{122 \: - \: 90} \times } \tt{ \: 20}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \frac{9}{32} \times } \tt{ \: 20}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \frac{9}{ \cancel{32}} \times } \tt{ \: \cancel{20}}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \frac{45}{ 8 }}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ \cancel \frac{45}{ 8 }}$

$\purple\dashrightarrow \footnotesize\tt{z = 60 \: + \: } \tt{ 5.625}$

$\purple\dashrightarrow \footnotesize\tt{z = 65.625}$