For each question that uses an interval or ratio scale, include a frequency dist

Question

For each question that uses an interval or ratio scale, include a frequency distribution chart, central tendencies (mean, median, and mode), and dispersion metrics (range, standard deviation – demonstrate the standard deviation calculation for at least the responses to one question). If you have an open-ended question or questions that use a nominal or ordinal scale, include a cross-tabulation table.

Do you enjoy what you do for work?

Semantic Scale No (0)----------(100) Yes Responses Number of People per Response 0 2 16 1 30 1 31 1 50 5 60 1 65 1 66 1 77 1 80 1 81 1 83 1 85 2 90 5 91 1 92 1 95 1 96 1 100 2

Explanation / Answer

here the variable is the responses(say X) and the corresponding frequencies are (number of people per response)

so frequency distribution chart is as follows

xi fi cumulative frequency(less than type) relative frequency(fi/sum(fi))

0 2 2 1/15

16 1 3 1/30

30 1 4 1/30

31 1 5 1/30

50 5 10 1/6

60 1 11 1/30

65 1 12 1/30

66 1 13 1/30

77 1 14 1/30

80 1 15 1/30

81 1 16 1/30

83 1 17 1/30

85 2 19 1/15

90 5 24 1/6

91 1 25 1/30

92 1 26 1/30

95 1 27 1/30

96 1 28 1/30

100 2 30 1/15

so mean=sum(xi*fi)/sum(fi)

=(0*2+16*1+30*1+31*1+50*5+60*1+65*1+66*1+77*1+80*1+81*1+83*1+85*2+90*5+91*1+92*1+95*1+96*1+100*2)/30

=67.7667 [answer]

median is the middle most value

there are all total 30 values.

so the median is that value of x which corresponds to the 15th value

now from the third column of the frequency distribution table we find that 80 corresponds to the 15th value

hence median is 80

mode is that value which has the highest frequency

50 and 90 have the highest frequencies(both equal to 5)

hence there are two modes: 50 and 90

range=max value - min value

now here max value is 100 and min value is 0

hence range=100-0=100

the standard deviation is given as

sqrt[sum(xi-mean(x))2fi/sum(fi)]

=sqrt[[(0-67.7667)2*2+(16-67.7667)2*1+(30-67.7667)2*1+(31-67.7667)2*1+(50-67.7667)2*5+(60-67.7667)2*1+(65-67.7667)2*1+(66-67.7667)2*1+(77-67.7667)2*1+(80-67.7667)2*1+(81-67.7667)2*1+(83-67.7667)2*1+(85-67.7667)2*2+(90-67.7667)2*5+(91-67.7667)2*1+(92-67.7667)2*1+(95-67.7667)2*1+(96-67.7667)2*1+(100-67.7667)22]/30]=29.04

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.