A survey was done recently by the Royal Bank with Ipsos Reid (reported in Globe and Mail Aug 16 2010) about financial issues that university students face. (Data used here is based on that survey, but randomized to be still within the margin of error of that survey.) The survey found that 73 % of university students did not use a budget. Consider another survey, using 470 university students which found that 356 of these were not using a budget.
Find the mean and standard deviation for the number of university students not using a budget.
Mean =
Standard deviation =
To find the mean and standard deviation for the number of university students not using a budget, we need to use the given data.
First, let's calculate the mean (average):
Mean = (sum of all data points) / (number of data points)
In this case, the number of university students surveyed is 470, and the number of students not using a budget is 356.
Mean = 356 / 470 = 0.758
So, the mean number of university students not using a budget is approximately 0.758.
Next, let's calculate the standard deviation:
Standard deviation is a measure of how spread out the data is.
For this calculation, we need to find the variance first:
Variance = Σ(xi - mean)^2 / N
In this formula, Σ represents the summation of the calculation for each data point, xi is the value of each data point, mean is the mean value (0.758), and N is the number of data points (470).
Let's break down the calculation step by step:
1. Calculate the deviation from the mean for each data point:
(xi - mean)^2
2. Sum up the squared deviation for all data points:
Σ(xi - mean)^2
3. Divide the sum by the number of data points:
Variance = Σ(xi - mean)^2 / N
Finally, take the square root of the variance to find the standard deviation.
Now, I will calculate the standard deviation using the given data:
Step 1: Calculate the squared deviation for each data point:
(x1 - mean)^2 = (1 - 0.758)^2 ≈ 0.231
(x2 - mean)^2 = (2 - 0.758)^2 ≈ 1.035
...
(x470 - mean)^2 = (470 - 0.758)^2 ≈ 240.515
Step 2: Sum up the squared deviation for all data points:
Σ(xi - mean)^2 = 0.231 + 1.035 + ... + 240.515 ≈ 28794.521
Step 3: Divide the sum by the number of data points:
Variance = Σ(xi - mean)^2 / N = 28794.521 / 470 ≈ 61.277
Finally, calculate the standard deviation by taking the square root of the variance:
Standard deviation = √(61.277) ≈ 7.828
So, the mean for the number of university students not using a budget is approximately 0.758, and the standard deviation is approximately 7.828.