Create a survey question that would gather quantitative data from the respondent

Question

Create a survey question that would gather quantitative data from the respondents. Create a new survey question where the phrasing Is unclear. Create a new survey question where the respondents are likely to lie. In a survey of our class, students were asked to "randomly pick a whole number between 1 and 20". Here are the responses. Complete and compute the following using this data. (a) Compute the following statistics. Be sure to use the correct symbol for the mean and standard deviation. Mean Median = Mode = Standard deviation = Q1 = Q3 = IQR = (b) Based on the mean and median, describe the shape of the data. Explain.

Explanation / Answer

1. a. One probable question might be: How many school going children do you have at your home?

b. One probable question might be: does any one you know in your family who rides a bicycle? This is an ambiguous question, as what is meant by family is not specifically mentioned by the interviewer. The family might include spouse and children, or parents, spouse and children or might be more extended one.

c. A probable question might be:how many times have you hidden your actual income while filing for tax?

2. Mode refer to most common score in the distribution. Mode is 17 and number of occurrence of mode is 7.

Standard deviation, s=sqrt[1/n-1 sigma (x-xbar)^2], where, n is sample size, x is the raw score, xbar is the sample mean.

s=sqrt[1/30-1 {(3-12.03)^2+(3-12.03)^2+...+(20-12.03)^2}]=5.49

First quartile is the median of the first half (upper portion of median) of the sorted data. That is averag of 8th and 9th number that is 7 [(7+7)/2]. Similarly, Q3 is the median of the second half (lower portion of median) of the sorted data. Thus, Q3 is 17.

IQR=Q3-Q1=17-7=10

Mean is less than median, which implies that distribution is slightly left skewed. For skewed distribution interquartile range is the best measure of dispersion.

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