Quantitative Business Analysis, Statistics Problem Example

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Statistics problem

Weighted Means

a.) Total: 3.95= ((5*180)+(4*100)+(3*60)+(2*40)+20)/400

b.)Male: 3.67= ((5*72)+(4*47)+(3*38)+(2*28)+15)/200

c.) Female: 4.23= ((5*108)+(4*53)+(3*22)+(2*12)+5)/200

d.)21-25: 3.93= ((5*58)+(4*34)+(3*22)+(2*12)+7)/133

e.)26-30: 4.28= ((5*74)+(4*37)+(3*13)+(2*7)+3)/134

f.)31-35: 3.63= ((5*48)+(4*29)+(3*25)+(2*21)+10)/133

Weighted Mean

This bar chart represents the weighted means for each group in the survey. There is one for every respondent, two for gender, and three for age group. 26-30 is the highest rating for age group and female is the higher of the two genders.

Rating Total Male Female 21-25 26-30 31-35
5 45% 36% 54% 43.6% 55.2% 36.1%
4 25% 23.5% 26.5% 25.6% 27.6% 21.8%
3 15% 19% 11% 16.5% 9.7% 18.8%
2 10% 14% 6% 9.0% 5.2% 15.8%
1 5% 7.5% 2.5% 5.2% 2.2% 7.5%
Percent of Total 100% 50% 50% 33.3% 33.4% 33.3%

Percent Frequency of Total

This bar chart represents the percent of respondents who gave the drink each rating. The numbers add up to 100% as all five possible rankings are present in this graph. The lower ratings have lower frequencies of responses.

Percent Bar Graph of Ratings, By Gender

In this graph, the percentage of each rating for both genders is displayed. Ultimately they both add up to 100%, with the size of the color within the bar displaying the percentage of responders by gender who gave that rating. Thirty six percent of males rated the drink a five, 23.5% said it was a four, nineteen percent said three, fourteen said two, and finally seven and a half percent said it was a one. For females, fifty four percent said it was a five, 26.5% went with four, eleven percent rated it as a three, six percent said two, and two and a half percent said it was a one. This shows that the drink is more popular amongst females than males.

Percent Rating By Age Group

This bar graph displays the percentage of each age group that gave individual rankings to the drink. The data is displayed above due to the fifteen different percentages that needed to be listed.

a.) .805=.540+.265

b.).595=.360+.235

c.) .692=.436+.256

d.).828=.552+.276

e.).578=.361+.218

The immediate thing about the data that jumps out to me is the lack of a bell shaped distribution. I would expect a three to be the most common rating, with ratings becoming less frequent the further they get from there. However, most ratings in each demographic are a five. In fact, there is a correlation between the rating and the frequency of itself. I imagine this is because of the subjective nature of the answers.

Breaking it down by demographics, females rated the beverage much more highly than males did. The 26-30 age group was the most favorable, with 21-25 after, and 31-35 much lower than the other two. Therefore, the most favorable demographic is women in the 26-30 range. However to know this for sure, the gender categories would have to be broken down into age groups themselves. Despite this, it is rather safe to say that females in the 26-30 and slightly less so 21-25 are the demographics to target.

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