QUESTION SUMMARY: –
In the statistics sample solution presented below, the expert has demonstrated our acumen in solving distinct problems on descriptive statistics. In this sample the expert has engineered the solution around one particular question. It asks the respondents to answer the question “whether they use household foods which is locally grown or produced.” The answer to this question by the respondents has been presented in a number of ways. Measures of central tendency, frequency distribution, pie chart, histogram, and confidence interval of the response has been presented by the expert. A frequency distribution of the response for household income less than and greater than $40,000 has also been presented.
The responses to the question were recorded in a nominal variable, which had several levels, like “Always”, “Often”, “Sometimes”, “Rarely”, “Never”, “Don’t Know”, “Refusal”, & “Not Stated”. The last three responses were also marked as missing in the data file while the first 6 response levels were mentioned as valid responses.
SOLUTION: –
Table 1: Descriptive Statistics of responses
N | Valid | 14578 |
Missing | 361 | |
Mean | 2.43 | |
Median | 2.00 | |
Mode | 2 | |
Std. Deviation | 1.016 |
Table 2: Frequency Distribution table of responses
PD_Q03 | Frequency | Percent | Valid Percent | Cum Percent | |
Valid | Always | 2550 | 17.07% | 17.49% | 17.49% |
Often | 5717 | 38.27% | 39.22% | 56.71% | |
Sometimes | 4531 | 30.33% | 31.08% | 87.79% | |
Rarely | 1074 | 7.19% | 7.37% | 95.16% | |
Never | 706 | 4.73% | 4.84% | 100.00% | |
Total | 14578 | 97.58% | 100.00% | ||
Don’t Know | 133 | 0.89% | |||
Missing | Refusal | 4 | 0.03% | ||
Not Stated | 224 | 1.50% | |||
Total | 361 | 2.42% | |||
14939 | 100.00% |
Of the total responses of 14,939, 14578 were classified as valid responses while the rest were judged as missing responses. The most common response (Mode of the distribution) is the response of “Often”, i.e. most frequent response to the question how often does a customer purchase locally grown/produced food, followed by sometimes.
The most common measure of central tendency of this distribution is the mode of the distribution, as it captures the most common response. The frequency helps one to understand the purchasing behaviour of the customer better. For example, we see that 56.71% of respondents respond that they purchase always/often locally grown/produced foods
As mentioned before, these figures illustrate the frequency distribution of the responses
Table 3: Confidence interval for valid percentages for responses
PD_Q03 | Number | Proportion | Margin of Error | Lower CI | Upper CI |
Always | 2550 | 17.49% | 0.62% | 16.88% | 18.11% |
Often | 5717 | 39.22% | 0.79% | 38.42% | 40.01% |
Sometimes | 4531 | 31.08% | 0.75% | 30.33% | 31.83% |
Rarely | 1074 | 7.37% | 0.42% | 6.94% | 7.79% |
Never | 706 | 4.84% | 0.35% | 4.49% | 5.19% |
# of Cases | 14578 | 100.00% |
These confidence intervals can be interpreted as follows:
- One can be 95% confident the population percentage of customers who always purchase foods advertised as locally grown/produced is between 16.88% and 18.11%
- One can be 95% confident the population percentage of customers who often purchase foods advertised as locally grown/produced is between 38.42% and 40.01%
- One can be 95% confident the population percentage of customers who sometimes purchase foods advertised as locally grown/produced is between 30.33% and 31.83%
- One can be 95% confident the population percentage of customers who rarely purchase foods advertised as locally grown/produced is between 6.94% and 7.79%
- One can be 95% confident the population percentage of customers who never purchase foods advertised as locally grown/produced is between 4.49% and 5.19%
Table 4: Frequency distribution of responses from respondents with household incomes less than $40,000
Frequency | Number | Proportion |
Always | 1311 | 45.27% |
Often | 684 | 23.62% |
Sometimes | 472 | 16.30% |
Rarely | 172 | 5.94% |
Never | 257 | 8.87% |
Total | 2896 | 100.00% |
Table 5: Frequency distribution of responses from respondents with household incomes greater than $40,000
Frequency | Number | Proportion |
Always | 4095 | 42.32% |
Often | 3025 | 31.26% |
Sometimes | 1497 | 15.47% |
Rarely | 586 | 6.06% |
Never | 473 | 4.89% |
Total | 9676 | 100.00% |
The proportion of households always buying locally grown/produced foods in both the groups of respondents is similar. However, the difference occurs in the households who report buying often locally produced foods is at 23.62% for households with incomes less than $40,000 but equal to 31.26% for households with incomes greater than $40,000.