Subjects statistics

Shop Ratings F2686E

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1. **Stating the problem:** We have two shops, Kirsty’s Kiosk and Oscar’s Outlet, each rated from 1 to 4 by customers. The bar chart shows frequencies for each rating, but bars E and F (one for each shop) are incomplete. 2. **Given conditions:** - Both shops have the same modal rating frequency. - Both shops have the same median rating. 3. **Understanding modal frequency:** The mode is the rating with the highest frequency. Since both shops have the same modal frequency, the highest frequency bars for both shops must be equal. 4. **Understanding median rating:** The median is the middle value when all ratings are ordered. Since ratings are from 1 to 4, the median depends on cumulative frequencies. 5. **Let’s denote:** - For Kirsty’s Kiosk, frequency of rating 2 is E. - For Oscar’s Outlet, frequency of rating 3 is F. 6. **From the problem, E = 1.5 and F = 1.5 (given).** 7. **Check modal frequency equality:** - Kirsty’s Kiosk modal frequency is the highest frequency among ratings 1 to 4. - Oscar’s Outlet modal frequency is the highest frequency among ratings 1 to 4. 8. **Check median equality:** - Calculate cumulative frequencies for both shops and find the median rating. 9. **Conclusion:** The frequencies of bar E and bar F are both 1.5. **Final answer:** $$E = 1.5, \quad F = 1.5$$